I agree, the ONLY thing that might have made a difference was to allow Anakin to go. But I'm not sure that would have even made a difference. Palpatine would have just played more of the "If I die then any chance you have to save your wife is gone." card and I think Anakin would have ended up doing the same thing anyways.
I terms of the actual fight, there would be no point to even bring additional Jedi for Mace. It's already stated in the DVD that Palpatine could have fried Mace when Palpatine was lightning him anyways, so Mace was gonna die no matter what, It just worked out in Palps favour to have Anakin turn at the same time is all.